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Full text of "AN EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER IN THE NOZZLE OF HIGH-ALUMINIZED SOLID ROCKET /EFFECTS OF ALUMINUM ADDED TO PROPELLANT/"

NASA TECHNICAL TRANSLATION 



NASA TT (--12,106 



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AN EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER 
IN THE NOZZLE OF HIGH-ALUMINI2ED SOLID ROCKET 
(EFFECTS OF ALUMINUM ADDED TO PROPELLANT) 

Tomlfumi Godai, YoshJnori Yuzawa 
Katuya Ito and Hisao Nishimura 






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Technical Report of National Aerospace Laboratory, 
TR-U7, Tokyo (Japan), I968, 10 pages 



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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
WASHINGTON, D.C. 205^6 FEBRUARY 1969 



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NASA TT F-12,106 



AN EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER 
IN THE NOZZLE OF HIGH-ALUMINIZED SOLID ROCKET 
(EFFECTS OF ALUMINUM ADDED TO PROPELLANT) 

Tomlfumi Godai^ Yoshinori Yuzawa 
Katuya Ito and Hisao Nishimura 



ABSTRACT. The heat transfer in the nozzle of a high-alumlnized 
solid rocket has been experimentally investigated. 

It Is noted that the addition of metallic fuel to the 
propellant has a pronounced effect on the heat transfer co- 
efficient but that the radiant heat flux Is not dominant In 
such a nozzle. 

It Js also notec that Bartz's treatment may be applied 
to the heat transfer problem in a mixed gas-particle flow, 
assuming that the gas-particle flow behaves like the gas flow 
with equivalent specific heat ratio »c. 

The equivalent specific heat ratio is obtained, where 
the velocity-lag of the particle behind the gas flow is 
negl igibly smal 1 . ' 

An experimental study was made of the heat transfer 
In a solid rocket mortar nozzle using a polybutadiene 
system composite propellant containing aluminum. It was 
found that the rate of heat transfer increases markedly as 
the alCiminum content In the propellant is increased, and 
that the effect of heat radiation of alumina particles was 
small. Moreover, in computing the heat transfer, the com- 
bustion gas flow containing alumina particles was treated as 
a single gas phase flow having mixed phases and equivalent 
specific heats, and it was found that the results of com- 
putattpn obtained by applying the semi-theoretical equation 
pertaining to turbulent flow heat transfer within a tube 
matches well with the experimental values. 



1. INTRODUCTION:. 



Charactei^istics such as the specific thrust of solid rocket propellants 
have improved greatly in recent years. There are reasons for this progress; 
we can consider advances in research on oxidants, fuel binders, and 
catalysts which are propellant components, together with the effects obtained 
by the addition of metal fuels such as aluminum powder to them. However, 
while the addition of metal fuels serves to improve the specific thrust, they 
make the heat conditions in the nozzle section more severe. In propellants 
containing large quantities of aluminum, there is much greater damage done 
to the nozzle throat section in comparison with propellants not containing 
aluminum, and ablation is particularly severe with plastic nozzles. Because 
of this it is considered to be the elevation of temperature of the combustio n 
•Numbers in the margin indicate pagination in the foreign text. ~ 



/V 



gas duo to the burning of the aluminum, and the effects of the coagulate! 
particles of alumina. It \s a well known fact that if one assumes that 
the combustion gas is a perfect gas, and that the reaction ^n the process 
of expansion in the nozzle is frozen, the results of computation obtained 
by application of Bartz's semi- theoretical equation [1,2] for turbulent flow 
heat transfer within a tube agree well with experimental values, in the case 
of a heat transfer within a rocket motor nozzle using propellants that do- 
not contain metal additives. However, the weight ratio of alumina in the 
combustion products in a propel lant containing 20% aluminum, reaches 
as much as 50%, and the method of treating the effects of this ratio poses 
a problem* 

We have conducted an experimental study of heat transfer in a solid 
rocket motor nozzle, using a polybutadiene system composite propellant, 
containing no aluminum, 10% aluminum and 20% aluminum, and have attempted 
to do a theoretical analysis of the results. 



/2 



2. SWBOLS; 



A: 

C : 
P 
D: 
E: 
F: 
I: 

I ; 
sp 

M: 

P: 

P : 

r 

Q: 

R: 

W: 

a: 

c: 

c*: 

d 

f 

g 
h 
k 

I 
m 
n 

q 

r 
t 
u 
Y 



Area . 
Specific heat at constant pressure 

Nozzle diameter 
Nozzle throat area ratio 
Thrust 

Volume ratio 
Specific Thrust 

Mach 

Combustion pressure 
Prandtl number 

Heat capacity 
Gas constant 
Weight 

Average cross section area of particle 
Specific heat 

Characteristic exhaust gas rate 
Particle diameter 
Configuration coefficient 
Acceleration of gravity 
Heat transfer coefficient 
Heat conductivity 
Distance 

Average inolecular weight of gas 
Number of particles per unit volume 
Heat transfer volume 
Radius of curvature of nozzle throat 
Time 
Velocity 
Specific Weight 



mm 



m^ 



mm 



1. 



• 

t • 


Monocliromatic radiation rate 


0: 


Temperature 


y: 


Viscosity coefficient 


p: 


Density 


o: 


Boltzmann's constant 


<: 


Specific heat ratio 


SUBSCRIPTS: 


c: 


Convection flows 


0' 


Gas 


c: 


Stagnation point 


P- 


Particle 


pp: 


Propel 1 ant 


r: 


Radiation 


t: 


Throat 


w: 


Wall 


z: 


Point 



3. METHOD OF EXPERIMENT 

In this investigation, it was decided to determine the rate of heat 
transfer by measuring the temperature changes of plugs placed perpendicular 
to the wall surface in several places within the nozzle. Many thermo- 
couples are required in this method, but it is well known that in cases such - 
as a solid rocket, the combustion time is relatively short, and it is 
possible to obtain highly acurate results in the case where it is difficult 
to obtain a thermally stable state [3]. 

If we consider here that the surrounding surface of the plug which is 
u?ed for measuring heat transfer is completely heat-insulated except on the 
heat transfer surface and in the c .tremity, it is possible to view the plug, 
in terms of heat, as a single dimension model. The increase in heat capacity 
per unit of time can be expressed as 



*-^wb°^A-T^\ ' "' 



since it is equal to the heat flux q which enters through the heated surface, I 

and if we assume that the heat loss from the outer end is ^j^ji ' 0. then the | 

rate of heat flow into a plug with a length, I, and a constant cross section | 
area, A, in the time interval between t^ and t2 is: | 

I 



4l»UliJi. l I ' l J -J ' . I ..Jl' W l ' I f ll H llli p 



Consequently, the heat transfer rate h is computed by 






(3) 



The plugs were made of. pure copper which have a high temperature 
conductivity, in order to avoid losses on the heating surfaces, and in 
order to minimize the heat exchange with the surrounding parts, the plug 
was placed in a nozzle made of the same material. 



/3 



-QZEZD-"*^ 



F!g, ^ 1: Model of Copper PI 



ug 



As shown in Figure 2, two models (I, II) with differing plug positions for 
temperature measurement were used for the nozzles that were tested, in 
model (I) the five points A, B, C, D, E, and in model (11) the five points 
A, B', C, D*. E' are the positions of plug attachment. In each case c 
corresponds to the throat section. 



Copper plugs 




MM 



Mmmm 



mmmmmm 



Position 
Noxzlc type 


Plug position and throat area ratio 




A 


B 
4$ 


B* 


C 
1.0 


h' 


D 


E' 


£ 




I 




10 




4.0 







11. « 




10 


LO 


1.3 




1«* 





Fig. 2: Cross Section and Plug 
Poslt'on in Nozzle Used fcr 
Measuring Heat Transfer 



As indicated in Figure 3, two holes one mm deep and 0,4 mm in diameter 
were made at a distance of 1 mm from each other on the periphery of one 
plug. After inserting an alumel wire 0.3 mm in diameter and a chromel wire 
of the same diameter into these holes, thermocouples were placed in four 
spots at distances of 8, 13, 20, and 28 mm from the end of the heated area. 
A total of 20 thermocouples ^^^ used. In order to reduce the area of 
contact of the plug and the nozzle wall, they were made to fit closely and 
the section of the plug protruding into the nozzle inner wall was shaved off, 
so that it was uniform with the nozzle inner wall. This means that the 
distance from the heated surface to the thermocouple differed from the 8, 
13, 20, and 28 mm described above, so after tests, these were measured 
acurately by removing the plugs. Furthermore, in order to reduce the heat 
fluctuation due to conduction currents in the space around the plug, the 
gap between it and the nozzle itself was reduced. 



L, 



■R 


f 28 

p— 20 — - 


J, 


^^^ 


b^^^^ 




— so 


t 




Fig, 3: Plug Configuration and Position of 
Thermocouple Insertlon^ 

The propellant used in the tests was a polybutadiene composite with 
ammonium perchlorate as the oxidant. The configuration is shown in Figure 4. 
The diameter is 93 mm, length 327 mm and weight 2.6 kg. Since the heat 
transfer rate differs depending on the combustion gas pressure, flow velocity 



mm 



\ { 



Register 
V 



Propcliant 




Fig. k: Configuration of Propellant 



I 



'"'W-^ n 







Fig. 5. 



and flow rate, the internal con- 
figuration of the propellant was 
selfjcted so that these values 
would remain as constant as 
possible during measurement of 
heat transfer, i.e. so that the 
thrust would remain as constant 
as possible. For the propellant 
three vaf'ielies were used, one 
not containing aluminum powder, 
one with 10% and one with 20% 
aluminum. The average particle 
diameter of the aluminum powder 
used was ]9 y. The propellant 
composition is shown in Table 1. 

The rocket motor burning 
test was conducted on a one ton 
lateral test stand in the solid 
rocket laboratory. Figure 5 
shows the rocket motor on the 
test stand. Resistance wire 
strain gauge type pick-up5 were 
used for measuring the thrusts 
and combustion pressure, and 
the apparatus was designed so 
that these measurements, along 
with measurements of temperature 
could be recorded on a direct 
vision electromagnetic oscil- 



/4 



lograph. The thermocouples used for measuring temperature throughout the 
measuring system, were calibrated at 20**C, 60*C and 80*C, with the melting 
points of tin, lead, and zinc prior to the tests. 

Table 1.: Composition of Propellent 



Propellanr 



Composition n^^gj^,-, ^uta- 



Aluminum 
Powder 



PropenantwithO%*Al 
Propellant with iO%* A] 
Propellant with 207(/* Al 




^Percentage increase to gross weight 

The burning tests for each propellant were conducted under conditions 
where IC. (ratio of combustion area to nozzle throat area) were constant. As 
explained below, for propel lants with a 0% and 10% aluminum content data were 
obtained for four burning tests, but in the case of propellant containing 
20% aluminum, in the two burning tests that were conducted, the nozzle throat 



m^ 



mmm 



was burned up 0.6 seconds after ignition both times. For this reason, for 
the propellant with 20% aluminum, the pure copper nozzle was replaced with a 
graphite nozzle and separate burning tests were conducted. 

4. Test Results 

The results of burning tests of each propellant are shown in Table 2 below. 

Table 2.: Burning Tests Results 



Type of Propellant ^ Propellant with Q^o Al ' Propellant with 10% Al Propr \ \ ant with 20% Al 

^""'"^.--■I?^^ : 1 T213 4il|2 3 A \ I \ I 3*' 



^_Test 
Observation"^'^-— -~^ ! 



Minimum Pressure V'min' 39.3 kg/cm»' 38.5 J 41.5 ! 41.2 j 48 S 



Maximum Pressure'/' mux 



Propellant Weight 
Specific Thrust * 






52,3 kgW 54.4 ; 55.1 I 59,5 I 69.5 
2.486 kg ^2.478 2.477 2.468 ,2.590 



213 sec 



- 211 



211 



49.5 53.3 

70.3 71.1 

2.585 2-576 



46.9 



2'6Z 



221 



226 



52.5 

70.3 

!2.545 2.676 2.683 
227 



53.7 



48.5 

60.2 

2.677 

226 



* Results from graphite nozzle 

One example of the tbrust-time curve is shown in Figure 6. In each case 
the thrust was SOU kg, the combustion pressure 50 kg/cm^, and the burning time 
was two seconds. It was decided to read the temperature data for calculating 
the heat transfer rate off the recording paper in the interval during which 
the burning state can be regarded as almost steady, avoiding the unsteady 
burning time* ipnediately after ignition, since the heat transfer rate is 
largely determined by the physical values of the gas. In Figure 7, the dis- 
tance from the thermocouple on the copper plug tj the nozzle wall is parted 
on the X-axis and the temperature at these points is parted on the y-axis 
(logarithmic axis). The wall temperature 9 is determined by extrapolation 

since it is expressed by a primary equation in a theoretically semi-loga- 
rithmic coordinate system, if one assumes that there is no loss from the 
periphery of the nozzle, and the heat transfer rate is also steady. Moreover, 
the temperature distribution between each measuring point within the plug 
is expressed as a primary equation, and the heat transfer volume i{ .At. + t ) 

was calculated from equation (2) . 



/5 



u 

400 


^-5-r:cr:-~-'='-«- — *^^^^ Propellant with 2 


*too 

100 

< 


wlthO^oAV \A \ 
Propellant with 10% Al ^-''^^^sJ^n^ 

-iV ■' l'6 L» zo ^ 



xy thrust 
Fig. 6: Thrust*-tlme Curves 



mmmm 




10 20 30 mm 

'*<* Distance from nozzle wall 



Fig. 7: Temperature Distribution 
on Plug at Point E* in the Case 
of a Propellant with 10^ Al 



5, ANALYSIS 

5.1 Alumina particles in combustion gas. 

It is considered that the diameter and size of alurriina particles pro- 
duced by the burning of aluminum gradually increase as the alun.ina themselves 
-collide and fuse together repeatedly within the nozzle f4, 5, 6], However* 
there are reports concerning the particle diameter of alumina which is 
ejected from the nozzle, stating that the diameter varies according to 
combustion pressure [7], and reports that the diameter is 2-3 y regardless 
of combustion pressure [8] . However, it is considered a fact that the 
diameter of the alumina particles varies according to the aluminum content 
in the propellant [9, 10]. 

Even if the diameter of the alumina particles in the nozzle increai -s 
due to collision and bonding, in the case of propellant containing 20% 
aluminum, it is reported that the diameter of particles ejected ;:hrougli the 
nozzle is below 4.5 p at a combustion pressure of 70 kg/cm' [10], and even 
if one calculates and compares the gas velocity and the alumina particle 



<»i tfr i ftMfa .iii> >Wiiii f-tf [ - "ir-if | ^f„.,^ ^'=^^Wff\^,ntv ,^ w \im 



sxi^'AJM aaaflaiiiSisaaa<i5affw,«iiMttMffti'niw^ 



velocity inside the nozzle, there is no great difference when the particle 
diameter is less than several u, and the temperature difference betwe^rn the 
gas and the alumina particljs is si.iall. 

Here we shall consider the flow in the nozzle on the basis of the 
following conditions. 

(1) There is no loss of mass or energy from the system. 

(2) There is no variation in mass between phases. 

(3) The alumina particles do not cause a reaction, and the volume 
occupied by them may be disregarded. 



(4) The gas is a constant component and is considered to be a perfect 



gas. 



(5) The specific heat of the gas and alumina particles is assumed to 
be constant. 

The energy equation for the gas and alumina particles is 



+ %[cpp(ffp'^po)+^tz/^^0 



n) /6 



As we have already noted, since the alumina particles that are produced are 
very small, if we a.ssume that the temperature difference and the velocity 
difference between the gas and the particles may be disregarded, we can find the 
equivalent specific heat ratio of the mixed flow of particle and gas k. If, 



in equation (4) we assume u 



u = u, 9 
g ' P 



0=0 
g 



.(5) 



Here, < is the specific heat ratio only for the gas phase. 

That is, we can regard the two phase flow of gas and particle as a gas 
phase in which the specific heat ratio is F. 



>f>'itttaay.»j;i:'AMMi?Wiiiti«tf ^ njk-imi -^t<agr tDjaV i r. tti r^ v :l^v « 



iWi<»r>wit^iiirt:^iirn'MtWi iM ''rnr \^j^itimkik uaio -iim r'7Tfi fA«i^,»^^^iUMiii^i'ii!»iiti>-'i''''^'^^^ i^^tiS^i^-iiiSiAitifiSimMi^i iWM'^^IB 



If we "consider the nozzle gas to be an ideal gas, the gas velocity in the 

nozzle u is 
g 



A/x V 



l-^~iA/x« 



l^~^^f^ 



*^ 



(6) 



If the specific heat ratio k is determined, it is possible to compute the 
Mach nuKiber M at point x with respect to the aperture ratio E* 

5.2 Physica? values of combustion products 

Since in this test we are not measuring the combustion gas temperature, 
specific heat ratio, or the average modular weight, these values were deter- 
mined from the results of tests on the composition of the propellant, combus- 
tion jpressure and specific thrusts, and from the literature [9, 10, li]. 

The specific heat ratio is calculated from equation (S) but the percen- 
tajge of alumina contained in the products of combustion in equation (5) W /iV^ 

was determined assuming that all of th^ aluminum underwent reaction in the 
propellant, forming alumina." The results are shown below in Table 3, 



I ■ 



Table 3: Alumina Weight Ratio in 5*3 Convection flow heat 
Products of Combustion transfer rate 

Considerable tests of heat 
transfer in nozzles of rocket 
motors, which do not contain 
powdered metal such as aluminum, 
have been made up to the pre- 
sent time, and semi-theoretical 
equations have been obtained. 
Of these, Bartz's equations 

agreed well with the test values, and are used in calculating heat transfer 

in nozzles. Tho convection flow heat transfer volume q 



- 


wp^k ^ 


Propellent with O^^AI 
Propellant with lO^o Al 
Propellant with 20% Al 



0.17 
0.48 



i<^hc(0g^0^) 



(7) 



Here^. using Bartz's semi-theoretical equation, the convection heat transfer 



rate h^ is 
c 



'^^ 



In this equation the heat transfer volume is validly determined by the per- 
centage of flow of mass per unit area. 



10 






rfrmriHifaittTyireiiMiww 



m 






-I 



The convection flow heat transfer was computed on the basis of (7) . 

5*^ Radiant Heat Transfer 

The radiant heat transfer volume q from the alumina particle cloud to the 
nozzle wall is expressed by the following equation. 

(10) 

As for the radiant heat transfer between particles, we consider the 
alumina particle to be spherical, and assuming that the temperature of a part- 
icle is almost equivalent to that of the neighboring particle, and that the 
heat transfer within the ambient gas is negatibly small, if we assume that heat 
transfer occurs only from the alumina particles to the nozzle wall, f = 1, and 
equation (10) becomes 

4r^'w-p'<r{e,^^0„*) (11) 

or ' 



'*,=l-e-n«t (12) I 

(See 12), j 

Expressing the gas velocity at a point where the nozzle inner diameter | 

is D as u , and the specific weight of the alumina particles as y , since j 

g P ^ 

the gas volume passing through the nozzle in a unit of time is j • D^ * u , the ) 

relative volume of the generated gas and the alumina particles I is I 

1 



-T- (13) 

W is the alumina particle volume of particles passing through the nozzle 
in a unit of time. 

(14) 
Whereupon, 

11 






,■ vi" 



FPV'TC'" 



6 ' 
Substituting equations (13) and (14) in equation (15) , 

na/=. ? ( ^P \ F 



(15) 



(16) 



Therefore, the effective radiation rate e of the alumina particle cloud can 

be determined, given small use of u , y , and d . Moreover, the radiation rate 
^ g p p 

of the nozzle wall z can be considered to be almost constant when the nozzle 

w 

wall temperature is below lOOO^C. From the above, the radiant heat transfer 
rate q can be computed by equation (11). 



A 



eo a- 






•Ai- • Fropcllant 
•Ai-io Propellant 



-g ^af- 



~« & 5l7 ai a5 t5 u ^T" 
*-•'*' Time (sec) 

Fig. 8: Variation in Heat 
Transfer Kate at Point A 






•Ai-M Propellant 
•ju-« Propellant 



6. Examination of Results ^9 

Figures 8 and 9 show variation in the 
heat transfer rate at points A and £• 
during combustion. This variation is 
almost stable with respect to the passage 
of time. This is because the flow rate 
of products of combustion passing through 
the nozzle during that interval is almost 
constant and as shown in Figure 10,. if 
we determine the heat transfer rates at 
0.5-0.6 seconds and 1.0-1.1 seconds and 
compare them, we see that they are almost 
constant regardless of the presence or 
absence of aluminum in the propellant. 



Figure 11 indicates the results of 
tests on the effect of the percentage 
of aluminum contained in the propellant 
on the heat transfer rate. Clearly, as 
the amount of aluminum is increased, the 
heat transfer rate shows larger values, 
in particular a value two times greater 
is indicated in the throat section. As 
for the heat transfer rate in the case of 
propellant containing no aluminum, 0.5-0.6 
seconds after ignition, as shown in Figure 12, the experimental values and the 
theoretical values for the convection flow heat transfer rate agree well, 
except in the fan-shapsd section of the nozzle. There is a good match between 
experimental and theoretical values 1.0-1.1 seconds after ignition, as sho\m 
in Figure 15, except in the throat section. Figures 13 and 14 show the distri- 
bution of the heat transfer rate in the case of propellant containing 10% and 



■* ii A — jfj — 5&I — 19 — i!5 — rt — tr 
Time (sec) 

Fig.. 9: Variation in Heat 
Transfer at Point E* 



12 



NM 



rffimrinpftimw 



fe-iWiWifniwirrrTijiinrirwMiMiinn^ii 



? 







ii-ii,-»-Aito«Propcllant 

j>ec-»-Ai Ki Propellant 

-««j-«-Aiic;5 Propellant 

eci^Ai 0:; Propellant 



T 



20% aluminum respectively, at 0.5-0.6 
seconds. It can be seen here, that there 
is a rather good match between computed 
values of conduction flow heat transfer 
and test values. The magnitude of the 
radiant heat transfer from the aluminum 
particles is smaller than the conduction 
flow heat transfer, but the computed va - 
ues in which corrections are made for 
radiation, indicate a closer approximation 
with respect to the test values. The 
radiant heat transfer rate is particularly 
great in the vicinity of the nozzle inlet. 
Figures 15 and 16 indicate the distribution 
of the heat transfer rate 1.0-1.1 seconds 
after ignition. Generally a slight dif- 
ference can be observed between theoretical and test values in the nozzle throat 
section, but this is considered to be due to scattering in the tests. 



RR' C 0* D E' E 

(Throat) 
Position inside nozzle 



rjg, 10: Comparison of Heat 
Transfer Rate in Nozzle at 
Time 0.5-0.6 Seconds and 
1 .0-1 . 1 Seconds 



4) 



Test results 




-Ai2o%Piopellant 

"Ano^ Propellant 

l^AiOfi Propellant 



1. u-n-u- 1 

y Position inside nozzle 



.2 

cd 
ti 




o Test values 

"Values ftom Bartz*s 
equations 0.5-0.6 seconds 



BB' 



C D' 



E' 



Position inside nozzle 



Fig. 11: Effect of Aluminum 
Content in Propellant on the 
Heat Transfer Rate in the Nozzle 
Section (Test Results 0.5-0.6 
Seconds after Ignition) 



Fig. 12: Heat Transfer Rate 
Inside Nozzle in the Case 
of Propellant w*th 0% Al 



1 i 



k»l/«tfl1C 



.«tt 4- 



X 



• Test values 
— Values from Bartz's 

A equation 
—-Values obtained when adding 
" ^' the radiation equation to 
Bartz*s 0.6-0.6 seconds 



heil/KUt; 




1 — a n-u- I 

, Position inside nozzle 



Fig, 13: Heat Transfer Rate Inside 
Nozzle in Case of Propellant with 
]0% Al 



■® Test values 
— Values from Bartz*s 

equation 
—Values obtained when 
adding the radiation equ- 
ation to Bartz*s equation 
0,6-0.6 seconds 



Position inside nozzle 

Ftg. \k: Heat Transfer Rate 
Inside Nozzle In the Case 
of Propellant with 20% Al 




13 



I . 

aiW Mir mm r 



glfflllWiTiiffiiWWirTHIJfii 



r>Miia|ytfittiiiiiBjifrfftfHi|-r!inBimwipni 



jtawiflitffTiftfiKnrirrfr 



^xtUmliC 




Test values 

Values from Bariz's 
equation 1.0-Ll seconds • 



TTSTT 

Position inside nozzle 

Fig. 15: Heat Transfer Rate Inside the 
Nozzle In the Case of Propellant with 
0* Al 



t<«l/»UX 




• Test values 

— Values from Bartz's 
equation 

— Values obtained by 
adding radiation equa- 
tion to Bartz's equation 
L 0-1.1 Seconds 



Fig, 16: 
Nozzle 
10* Al 



Position inside nozzle 



Heat Transfer Rate Inside the 
in the Case of Propellant with 



7. Conclusion 

. The following facts were deter- 
mined from this experimental study. 

(1) There is a marked increase 
in the heat transfer rate inside 
the nozzle as the amount of 'alum- 
inum contained in the propellant 

is increased. 

(2) Even when the propellant 
contains 20% aluminum, the influ- 
ence of radiation from aluminum 
particles on the nozzle heat trans- 
fer is small, the major influence 
being from conduction flow heat 
transfer. 

(3) The computed values for 
the conduction flow heat transfer 
almost match the test values when 
computed using Bartz*s semi-theo- 
retical equation, even for propel- 
lant containing large amounts of 
aluminum, if we assume the mixed 
flow of gas and alumina particles 
go through the nozzle as a gas 
phase with an equivalent specific 
heat ralio F. 



Finally, we would like to express 
our gratitude to the personnel in 
the rocket division beginning with Division Chief Kuroda, and to Technical 
Officer Sekine of the Engine Section for their guidance and cooperation through- 
out this study. 



REFERENCES 

1. Bartz, D. R», "A Simple Equation for Rapid Estimation of Rocket Nozzle 

Convective Heat Transfer Coefficients'/ Jet Propulsion^ p. 49, Jan. 1957. 

2, Bpttz, D, R., "An Approximate Solution of Compressible Turbulent Boundary- 

layer Development and Convective Heat Transfer in Convergent-Divergent 
Nozzles, "Transactions of the ASME, pp, 1235-1245; November, 1955, 

3. Liebert, C. H,, J. E. Hatch and R. W. Grant, "Application of Various 

Techniques for Determining Local Heat Transfer Coefficient? in a Rocket 
Engine from Transient Experimental Data", NASA TN 0-^2??, 1960. 

4, Sehgal, R., "An Experimental Investigation of a Gas Particle System," 

Jet Propulsion Lab TR''32-238, 1962. 

14 



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Msm 



5. Brown, fi. and F. P. McCarty, "Particle Size of Condensed Oxide from Com- 

bustion of Metallized Solid Propellant," P/oceedings of the 8th Inter- 
national Combustion Symposium, pp* 814-823, 1962, 

6. Crowe, C. T. and P. G. Willoughby, "A Study of Particle Growth in a Rocket 

Nozzle", AIAA Paper 66-639, 1966. 

7. Cheung, H. and N, S. Cohen, "On the Performance of Solid Propellants Con- 

taining Metal Additives," AIAA preprint, 64-116, 1964. 
S. Crowe, C. T. and P. G. Willcughby, "A Mechanism for Particle Growth in a 

Rocket Nozzle," j1IA4 Journal, pp. 1677-1678, Sept. 1966. 
9. Sutton, G, P,, Rocket Prop74lsion Elements, John Wily § Sons, 3rd pp. 174- 

177, 1963. 

10. Ciepluch, C. C, "Spontaneous Reignition of Previously Extinguished 

Solid Propellants," NASA TN D-216?, 1963. 

11. Zeleznih, F. J. and S. Gordon, "A General IBM 704 or 7090 Computer 

Program for Computati'^n of Chemical Equilibriu ' Composition. Rocket 
Performance and Chapmann-Jouget", MSA TN D-14S4, 1962. 

12. Hottel, H. C, "Radia>xt-Heau Transmission^* in Heat Transmission,McMms ed. 

1954. 



Translated for the National Aeronautics and Space Administration under Contract 
No. NASw-1695 by Techtran Corporation, P.O. Box 729, Glen Burnic, Maryland 
21061 



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